We study an open model of hypercyclic replication taking into account the spatial distribution of macromolecules under the action of homogeneous diffusion processes. The aim of our paper is to analyze the limit behavior dynamics and the stability of stationary solutions for the distributed hypercycle system as well as for the autocatalytic replication system, which arises in the problem on the natural selection in a set of competing hypercycles in the course of evolution.[PUBLICATION ABSTRACT]
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